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Modeling individual differences in response time and accuracy in numeracy.

ABSTRACT: In the study of numeracy, some hypotheses have been based on response time (RT) as a dependent variable and some on accuracy, and considerable controversy has arisen about the presence or absence of correlations between RT and accuracy, between RT or accuracy and individual differences like IQ and math ability, and between various numeracy tasks. In this article, we show that an integration of the two dependent variables is required, which we accomplish with a theory-based model of decision making. We report data from four tasks: numerosity discrimination, number discrimination, memory for two-digit numbers, and memory for three-digit numbers. Accuracy correlated across tasks, as did RTs. However, the negative correlations that might be expected between RT and accuracy were not obtained; if a subject was accurate, it did not mean that they were fast (and vice versa). When the diffusion decision-making model was applied to the data (Ratcliff, 1978), we found significant correlations across the tasks between the quality of the numeracy information (drift rate) driving the decision process and between the speed/accuracy criterion settings, suggesting that similar numeracy skills and similar speed-accuracy settings are involved in the four tasks. In the model, accuracy is related to drift rate and RT is related to speed-accuracy criteria, but drift rate and criteria are not related to each other across subjects. This provides a theoretical basis for understanding why negative correlations were not obtained between accuracy and RT. We also manipulated criteria by instructing subjects to maximize either speed or accuracy, but still found correlations between the criteria settings between and within tasks, suggesting that the settings may represent an individual trait that can be modulated but not equated across subjects. Our results demonstrate that a decision-making model may provide a way to reconcile inconsistent and sometimes contradictory results in numeracy research.

SUBMITTER: Ratcliff R

PROVIDER: S-EPMC4353499 | biostudies-literature | 2015 Apr

REPOSITORIES: biostudies-literature

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Modeling individual differences in response time and accuracy in numeracy.

Ratcliff Roger R Thompson Clarissa A CA McKoon Gail G

Cognition 20150129

In the study of numeracy, some hypotheses have been based on response time (RT) as a dependent variable and some on accuracy, and considerable controversy has arisen about the presence or absence of correlations between RT and accuracy, between RT or accuracy and individual differences like IQ and math ability, and between various numeracy tasks. In this article, we show that an integration of the two dependent variables is required, which we accomplish with a theory-based model of decision maki ...[more]

PMID: 25637690

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Project description:The most common process variable available for analysis due to tests presented in a computerized form is response time. Psychometric models have been developed for joint modeling of response accuracy and response time in which response time is an additional source of information about ability and about the underlying response processes. While traditional models assume conditional independence between response time and accuracy given ability and speed latent variables (van der Linden, 2007), recently multiple studies (De Boeck and Partchev, 2012; Meng et al., 2015; Bolsinova et al., 2017a,b) have shown that violations of conditional independence are not rare and that there is more to learn from the conditional dependence between response time and accuracy. When it comes to conditional dependence between time and accuracy, authors typically focus on positive conditional dependence (i.e., relatively slow responses are more often correct) and negative conditional dependence (i.e., relatively fast responses are more often correct), which implies monotone conditional dependence. Moreover, most existing models specify the relationship to be linear. However, this assumption of monotone and linear conditional dependence does not necessarily hold in practice, and assuming linearity might distort the conclusions about the relationship between time and accuracy. In this paper we develop methods for exploring nonlinear conditional dependence between response time and accuracy. Three different approaches are proposed: (1) A joint model for quadratic conditional dependence is developed as an extension of the response moderation models for time and accuracy (Bolsinova et al., 2017b); (2) A joint model for multiple-category conditional dependence is developed as an extension of the fast-slow model of Partchev and De Boeck (2012); (3) An indicator-level nonparametric moderation method (Bolsinova and Molenaar, in press) is used with residual log-response time as a predictor for the item intercept and item slope. Furthermore, we propose using nonparametric moderation to evaluate the viability of the assumption of linearity of conditional dependence by performing posterior predictive checks for the linear conditional dependence model. The developed methods are illustrated using data from an educational test in which, for the majority of the items, conditional dependence is shown to be nonlinear.

Project description:BACKGROUND:Thrombocytopenia is a major side-effect of cytotoxic cancer therapies. The aim of precision medicine is to develop therapy modifications accounting for the individual's risk. METHODOLOGY/PRINCIPLE FINDINGS:To solve this task, we develop an individualized bio-mechanistic model of the dynamics of bone marrow thrombopoiesis, circulating platelets and therapy effects thereon. Comprehensive biological knowledge regarding cell differentiation, amplification, apoptosis rates, transition times and corresponding regulations are translated into ordinary differential equations. A model of osteoblast/osteoclast interactions was incorporated to mechanistically describe bone marrow support of quiescent cell stages. Thrombopoietin (TPO) as a major regulator is explicitly modelled including pharmacokinetics and-dynamics of TPO injections. Effects of cytotoxic drugs are modelled by transient depletions of proliferating cells. To calibrate the model, we used population data from the literature and close-meshed individual data of N = 135 high-grade non-Hodgkin's lymphoma patients treated with CHOP-like chemotherapies. To limit the number of free parameters, several parsimony assumptions were derived from biological data and tested via Likelihood methods. Heterogeneity of patients was explained by a few model parameters. The over-fitting issue of individual parameter estimation was successfully dealt with a virtual participation of each patient in population-based experiments. The model qualitatively and quantitatively explains a number of biological observations such as the role of osteoblasts in explaining long-term toxic effects, megakaryocyte-mediated feedback on stem cells, bi-phasic stimulation of thrombopoiesis by TPO, dynamics of megakaryocyte ploidies and non-exponential platelet degradation. Almost all individual time series could be described with high precision. We demonstrated how the model can be used to provide predictions regarding individual therapy adaptations. CONCLUSIONS:We propose a mechanistic thrombopoiesis model of unprecedented comprehensiveness in both, biological mechanisms considered and experimental data sets explained. Our innovative method of parameter estimation allows robust determinations of individual parameter settings facilitating the development of individual treatment adaptations during chemotherapy.

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Modeling individual differences in response time and accuracy in numeracy.

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Modeling individual differences in response time and accuracy in numeracy.

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